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    Concrete representation of martingales

    Montgomery-Smith, Stephen, 1963-
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    [PDF] ConcreteRepresentationMartingales.pdf (166.4Kb)
    Date
    2011
    Format
    Preprint
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    Abstract
    Let (fn) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (dn) from [0,1]n such that ∫01 dn(x1,...,xn) dxn = 0 for almost all x1,...,xn-1, and such that the law of (fn) is the same as the law of (∑k=1n dn(x1,...,xn)). Similar results for tangent sequences and sequences satisfying condition (C.I.) are presented. We also present a weaker version of a result of McConnell that provides a Skorohod like representation for vector valued martingales.
    URI
    http://hdl.handle.net/10355/9728
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